Embeddings of rearrangement invariant spaces that are not strictly singular

被引：7

作者：

Montgomery-Smith, SJ ^{[1
]}

Semenov, EM

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Voronezh State Univ, Dept Math, Voronezh 394693, Russia

来源：

POSITIVITY | 2000年 / 4卷 / 04期

关键词：

rearrangement invariant space; strictly singular mapping; Rademacher function; Orlicz space;

D O I：

10.1023/A:1009825521243

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L-1([0,1]) is strictly singular if and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L-Phi with Phi>(*) over bar * (x) = exp(x(2))-1.

引用

页码：397 / 402

页数：6

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